Planimeter.



K. KEELER. PLANIMETER. APPLICATION FILED Armzz, 1914.

Patented Mar. 2, 1915 IIIIIIIIII www( THE MORRIS vPETERS CO PHOTO-1.17710.. WASHING rvN. D C' K. KEBLER.

PLANIMBTBR. APPLICATION PILB'D APR.zz, 1914.

2 SHEETS-SHEET 2.

@wu-mm@ THE MORRIS PETERS C0., PHOTO Llno.. WASHINGION D. C.

Patented Mali. 2, 1915.

KARL KEELER, OF ANN ARBOR, MICHIGAN. I

PLANIMETER.

Maaate. I

Specification of Letters Patent.

Patented Mar. 2, i915..

Application led April 22, 1914. Serial No. 833,686.

To all whom t may concern.'

Be it known that l, KARL Kunnen, a citizen of the United States, residing at Ann Arbor, county of Washtenaw, and State of Michigan, have invented certain new and useful Improvements in Planimeters, of which the following is aspecification.

This invention relatesto planimeters.

The present invention, which l call a field integraph, is based upon the well known mathematical rule that the area of a sector is directly proportional to its angle and to the square of its radius, the rule being that the area of any sector equals 950W, in which t) is the angle of the sector measured in radians and r the radius of the sector.

The present invention has for its object the provision of a portable instrument of simple construction, embodying a novel principle of operation, which can be taken into the field where a given area is to be calculated and utilized to automatically calculate and indicate the area of a surface lying in any plane, without requiring` computation.

The invention embodies an extensible device, such as a tape, wire, or cord, which can be drawn out to any desired extent, a sight-- ing device by which the end of the drawn out tape, cord or wire or any predetermined part thereof may be observed, and an automatically acting indicating means coperating with the cord, tape or wire and the sighting device, so that the angle traversed by the sighting device in taking the observation, combined with the length or distance to which the cord, tape or wire is extended, determines the operation of the means cooperating therewith and as a result the correct indication of area is either directly shown or indicated vernier fashion.

ln accordance with the requirements of the statute, l have shown in the drawings and hereinafter explained an embodiment of the invention which is adapted to carry out the principle thereof, but I am aware that changes of construction can be resorted to in carrying out the principle of the invention and ll. do not, therefore, restrict myself to the details of the mechanism set forth, but on the contrary, claim all variations within the spirit and scope of the invention.

lin the accompanying drawings: Figure l is a perspective of the complete invention; Fig. 2, a similar view looking toward the .(Fig. 6). Bearing opposite side of the instrument; Fig. 3, a detail side elevation of the carriage and shaft carried thereby; Figs. 4C and 5, details of the sight and its connections; Fig. 6, a

detail of the step bearing for the lower` nected by`cross frame members R1 R2.

Journaled in the frame members Q, Q2 is a shaft W having a drum D and a pinion H1, as also an operating crank or handle F secured thereto. Wound on the drum D is a tape or wire D1 which has one end connected thereto and its other end free as at D2 which is adapted to be drawn out to any desired point. Secured to the frame member R3 is a spring K which carries a cross bar and pad U that is pressed against the wire D, by the action of the spring, thus preventing any looseness of the wire on the drum D and also preventing it from unreeling too fast. The pad acts as a brake to aford a necessary degree of friction for the above purpose. Journaled yin the frame members Q,- Q, is a shaft V to which is secured a cylindrical cam C having a cam groove C1. Secured to the shaft V is a reducing gear H, which is in mesh with the pinion H, and by which a number of revolutions of the shaft W and drum D, due to the extension `of thewire or tape 1),. are required to cause the gear H2, shaft V and cam C to'make one complete revolution. Connected to the frame members Q, Q2 are guide rods S2 to which a carriage G is slidably connected by the supports S1. The carriage G has a pin N .which is secured thereto but may be adiusted lengthwise thereof or perpendicular thereto by the prgvvision of a slot and clamping means for the pin (Fig. 7). Carried by the bars lt, R., are bearings l and J, respectively, the latter having an adjustable step bearing P .l is adiustable lengthwise or crosswise of bar R2 and secured. where adjusted, bv set screws J. Journaled in the bearings I and J by the shaftsB1 and A, are disks B and A, respectively. Disk B is provided with a circular rack B2.

. (Figll)-v Disk A is graduated on its edge, as at A', for reading, from a Vernier A2, of the area indicated.

Referring to Figs. l and 5, a shaft X is j ournaled in the frame-piece Q2 and carries a pinion 0 which meshes with the rack B2 Secured to the shaft X is a sight E which may be a tube with cross wires, or an open sight having cross wires may be substituted. Shafts X, X, have pinions X2, X3. Shaft X and the sight E are carried by a bracket X4 which is pivotally mounted on a stub shaft X5 having thumbclamping nut X6. An idle gear X7 meshes with pinions X2, X3. On loosening the nut X6, the bracket X4 swings in a vertical plane and the sight E can then be swung on its shaft X in any plane in which it may be positioned.

Carried by suitable bearings on the carriage G is an inclined shaft T which carries at its upper end a friction Wheel M and at its lower end a friction wheel L (Fig. 3). These Wheelsl are constantly in frictional contact with the disks B and A, respectively. The point or pin N is received in the cam groove C,l of cam C and consequently, the rotation of that cam shifts the carriage G on its guides S2.

Among the changes which might be resorted to in carrying out my invention. the drum D may be placed above the disk B; in substitution for the pinion H1 and gear H2, there may be provided a series of gears as shown in Fig. 8, or a worm gearing as in Fig. 9. These changes are not to be considered as the only ones which I contemplate, but merely as illustrative, as I lay claim to all modifications adapted to carry out the objects and to embody the principle of the invention.

In using the instrument to determine the area of a piece of ground, for instance, it will be set up at a suitable point. One operator will stand at the instrument and the other will extend or pull out the wire D, to ltrace the outline or boundary of the area to be measured by following such outline or boundary with the end D2 or with any other predetermined part of the wire or tape. The wire or tape mustextend tautly in a straight line from its end D2 to the instrument. The operator at the instrument constantly observes the end D2 through the sight E as the other operator traces the kboundary of the area. Resistance to the pulling out of the wire may be had by checking its unreeling by they handle F, but such handle is primarily intended for winding up the wire on the drum D.

When the boundary or outline of the surface being measured has been traced by the end D2, the area of the surface may be read from the vernier and the graduations on the disk A, which indication is brought about as follows: As the tape or wire D1 is unwound from drum D, it causes revolution of shaft W, which in turn, through gears H1 H2, (or other gearing used) causes revolution of cam C. The revolution of cam C, by reason of the reception Iof point N in groove C1, causes the carriage G to shift parallel to shaft V. Now, the operator at the instrument is moving the sight E as he follows with his eye the end D2 on the end of the wire D1 and as the sight E is moved, the spindle X is turned, which causes turning of the pinion C and thereby causes turning of the disk B. The revolution of the disk B or any movement thereof is communicated to the shaft T by the friction wheel M and by the friction wheel L to the disk A. It will be seen, therefore, that the unwinding of the tape directly results in the shifting of the carriage G and the position of the friction wheels L and M in relation to the disks A and B, whereby the ratio of the radius of each disk to the radius of its friction wheel is changed according as the tape or wire is let out or taken up. Now, the angle through which the disk A revolves is dependent both on the position of the carriage Cr and the angle through which the disk B is revolved by the movement of the sight E. Consequently, the

angle through which the disk A revolves is dependent both on the length of tape or wire D1 unwound and the angle through which the sight E is turned. The length to which the tape D1 is pulled out and the angle to which the sight E is turned both depend upon the distance of the boundary or outline of the surface from the instrument. Given, therefore, the angle and the radius, the mechanism automatically computes the area which is directly indicated on the disk A in reference to any fixed point on the instrument, or vernier fashion.

Reference is to be had to Fig. 10 for a diagrammatic showing of the use of the instrument in computing an area. In this figure there is represented the cross-section of a proposed canal or railroad cut or excavation, where a, c d represents the surface of the ground; a Z) the left bank; c the bottom; and c d the right bank of the cut. It being desired to ascertain the number of square yards of area. in a 7) c cl c, it will be understood that the said area plus the area a e Z I equals the area a 0 d I. Now, the area a c al I is bounded by known straight lines and is, therefore, readily calculable. Consequently, if the area a c (Z I is known, it may be subtracted from the readily calculated total area a Z) c (l I and the result will be the desired area a b c d e. Now, the present invention being adapted to determine the area a e al I, the desired area a c al c can be readily obtained.

Let I represent the present invention and the light lines radiatin from I the various positions of the extensi le wire or tape D1. '.lhe light lines, together with the dotted arcs, form sectors, and the area of each sector equals Y0112 in which 0 equals its angle in radians, and r2 equals the square of its radius. Now, let la represent the first position of the wire or tape and l2 its second position after being swung through the angle 6. The sight e is at all times kept pointing to the end l)2 of the tape or wire and hence, the sight will also be swung through the same angle 6; further, the area of the sector lazequals elft, and when the wire or tape has reached its second position, l2, the area of the sectorlla2 will be indicated at the Vernier A2 of the instrument. Let the wire end be extended along I, until it touches the ground at 3 and then swung to position 14'; at this point the area indicated by the instrument will equal the sum of the areas of the two sectors letz and 1M. This series of operations is carried on until the wire or tape inaly reaches the position ils; at this point the area indicated by the instrument will equal the sum of the areas of all the sectors, which sum is approximately equal to the area a e d I. Now, assuming the number of light lines to increase, thefnumber of sectors would also increase, and the size of the angles of the sectors would decrease, and the sum of the areas of the sectors would finally equal the area ae d l. It will be seen, therefore, that if the end D2 of the wire or tape is made to follow the outline of the area and the sight made to point to the end of the wire, at all times, the area indicated by the instrument is the area swept over by the wire.

rl`he sight is arranged to turn in any plane by the means shown in Figs. 4 and 5 and the swinging of the entire instrument on its tripod which enables calculation of a surface lying in any plane to be made.

Having thus described my invention, what I claim as new and desire to secure by Letters Patent, is: l

l. ln a planimeter, the combination with a wire or tape, of. means whereon the tape is adapted to wind and unwind, a movable sight for observing the drawn-out part of said wire or tape, and indicating means cooperating with the sight and the wire or tape winding means whose action is controlled thereby and which is adapted to automatically indicate area by the relationship of the effective drawn-out length of the wire or tape to the angle traversed by the sight in observing said effective length of the wire or tape.

' Copies of this patent may be obtained for ive cents each, by addressing the 2. In a planimeter, the combination with a drum and a wire or tape wound thereon and adapted to be drawn 0H therefrom, of a swinging4 sight adapted for observing the drawn out part of the wire or tape, and mea-ns coperating with said sight and said drum adapted to automatically indicate area by the relationship of the effective drawn out length of the wire or tape to the angle traversed by the sight in observing said effective length of the wire or tape.

3. ln a planimeter, the combination with an extensible device, of a movable sight for observing said extensible device, a carriage adapted to be shifted by the movement of the extensible device, an indicating wheel, a rotatable member carried by the carriage and adapted to coperate with said indicating wheel, and means controlled by the movement of the sight adapted for rotating said rotatable member.

4. 1n a planimeter, the combination with an extensible device, of a movable sight for observing said extensible device, a carriage adapted to be shifted by the movement of the extensible device, an indicating wheel, a rotatable member carried bv the carriage and adapted to co'o'perate with said indicating wheel, a wheel with which the movable sight coperates, and an operative connection between said last-named wheel and the rotatable member.

5. ln a planimeter, the combination with a drum, of a wire or tape wound thereon and adapted to be drawn out therefrom, a cam operated by said drum, a shiftable carriage having means coperating with the cam whereby the carriage is shifted by the movement of said cam, a shaft carried by said carriage, indicating and transmitting disks, wheels carried by the shaft which engage the said disks. said carriage being adapted to position the wheels differently at different times in relation to said disks bv the action of the cam aforesaid, a movable sight adapted for observing a predetermined point on the unreeled part of the wire or tape. and means cooperating with the sight and with the transmitting disk. whereby the length of wire or tape unreeled from the drum and the angle traversed by the sight coniointly determine the indication on the indicating disk.

ln testimony whereof. I hereunto aliix my sigmature in presence of two witnesses.

- KARL KEELER. Witnesses:

C. E. BARTHELL,

Mrs. KARL KEELER.

Commissioner of Patents,

Washington, D. C. 

